Several results concerning the existence and uniqueness of solutions of Ito SDE's in a real separable Hubert space have recently been reported. In this work we first obtain the existence and uniqueness of strong solutions to (not necessarily) Ito SDE's in a Hubert space under Lipschitz-type conditions on the coefficients. We assume usual continuity and linear growth conditions. For non-Lipschitz coefficients an approximation technique of Gikhman and Skorokhod is then used to prove the existence of weak solutions taking values in a larger Hubert space H-\. This result depends on an assumption that H can be compactly embedded in H-\, such that the coefficients satisfy regularity conditions with respect to H-\. This assumption is not a limitation to our method as it is necessary even in the deterministic case. Additionally, we prove the existence of martingale solutions to infinite dimensional semilinear SDE's. In both cases, coefficients F(£, ·) and J9(£, ·) may depend on the entire past of X £ C([0, T], H) and not on the value of x(t) alone.Brought to you by | provisional account Unauthenticated Download Date | 7/2/15 1:26 AM

In this work, we consider the problem of moving average representations for random fields. As in the Kolmogorov–Wiener case, such representations lead to interesting questions in harmonic analysis in the polydisc. In particular, we study outer functions with respect to half-space, semigroup and quarterplane and their interrelations.